The graded Witt group kernel of biquadratic extensions in characteristic two

AbstractLet k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack Ĝ over k, the metaplectic extension of the Greenberg realization of $\operatorname{\mathbb{S}p}_{2n}(R)$. We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.

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Separable extensions of orthogonal involutions in characteristic two

Journal of Algebra ◽

10.1016/j.jalgebra.2017.12.013 ◽

2018 ◽

Vol 501 ◽

pp. 44-50 ◽

Cited By ~ 1

Author(s):

A.-H. Nokhodkar

Keyword(s):

Characteristic Two ◽

Separable Extensions

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Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

Algebra Colloquium ◽

10.1007/s100110300008 ◽

2003 ◽

Vol 10 (1) ◽

pp. 63-74 ◽

Cited By ~ 1

Author(s):

Changli Ma ◽

Yangxian Wang

Keyword(s):

Finite Field ◽

Quadratic Forms ◽

Association Schemes ◽

Characteristic Two

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The Witt group of a discretely valued field and the fundamental filtration

Journal of Algebra ◽

10.1016/j.jalgebra.2021.09.027 ◽

2021 ◽

Author(s):

Jón Kr. Arason

Keyword(s):

Witt Group ◽

Valued Field

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Isotropy of orthogonal involutions in characteristic two

Journal of Algebra and Its Applications ◽

10.1142/s0219498818502407 ◽

2018 ◽

Vol 17 (12) ◽

pp. 1850240 ◽

Cited By ~ 1

Author(s):

A.-H. Nokhodkar

Keyword(s):

Quadratic Form ◽

Central Simple Algebra ◽

Simple Algebra ◽

Characteristic Two ◽

Central Simple ◽

The Given

A totally singular quadratic form is associated to any central simple algebra with orthogonal involution in characteristic two. It is shown that the given involution is isotropic if and only if its corresponding quadratic form is isotropic.

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